A Finiteness Theorem for Gromov-Hyperbolic Groups

Explore a rigorous mathematical lecture on the finiteness theorem for Gromov-hyperbolic groups presented by Gérard Besson from CNRS - Université Grenoble Alpes. Delve into the proof that there exists a finite number of isomorphism classes of marked groups (Γ,Σ) satisfying specific conditions: δ-hyperbolic, torsion-free, non-cyclic, and with entropy bounded by a given value H. Gain insights into key concepts such as δ-hyperbolicity, torsion-free groups, and entropy in the context of finitely generated groups with symmetric finite generating sets. Follow along as Besson breaks down the abstract, explains crucial terminology, and provides an overview of the proof's key elements in this Stony Brook University Mathematics Colloquium talk.